Design fault maybe ?
Many amps can behave unpredictably as the rails collapse, and if it causes any noise in the speaker then imo the design is incomplete as an amp should be totally silent on power up and power down. It's an age old problem. Does it do it in isolation... with just speakers and the supply and with no inputs connected.

It's an age old problem, so what are the possible causes? My DAC does that when shut down after running for hours but not if it has only run for a short time.

The circuit design itself is the cause. It doesn't mean there is a problem, just that it behaves unpredictably as the rails collapse. There can even be a "race hazard" situation where multiple rails collapse at different rates... countless reasons really. There is no single fix or cure. There are examples of commercial amps that have had time constants changed to try and prevent such problems after customers complained... but the real answer is the design should be complete such that this either doesn't happen or is muted.

A DAC should have muting that operates within a few milliseconds of power down to prevent noises. I can think of some transistor radios that have done this, certainly several TV audio output stages over the years.